Problem $4.$ Water at atmospheric pressure is de$-$aerated and preheated in a tank at an elevation of $z_s=2\mathrm{.}0m$ above a feed$-$water pump that delivers it to a boiler to produce steam as shown. The pump suction inlet and pump discharge inside diameters are $D_s=10cm$ and $D_d=7\mathrm{.}5cm,$ respectively. To determine the net positive suction head required, $NPS{H}_R,$ an additional valve is placed upstream of the pump suction inlet and adjusted until cavitation just begins to occur. During testing using water at STP when the pump is operated at a volumetric flowrate of $Q=0\mathrm{.}025\frac{m^3}{s},$ against a head of $H_p=25m,$ cavitation is observed to begin when the pressure gage at the suction inlet reads $p_{s,\text{g}\text{a}\text{g}\text{e}}=1\mathrm{.}0$kPa. $($a$)$ Calculate the $NPS{H}_R$ for these test conditions. $($b$)$ Calculate the gage pressure reading at the pump discharge. $($c$)$ Assuming negligible major and minor losses before the suction inlet, calculate the net positive suction head available, $NPS{H}_A,$ when the pump is operated in the field at the same $Q$ and $H_p,$ but for a water temperature of $T_f=90C.($d$)$ Briefly discuss if the pump will cavitate for these field conditions, how your answer changes with $T_f,$ and three ways to reduce the likelihood for cavitation to occur.

Answers: $($a$)10\mathrm{.}8$ m$,($b$)235$ kPa, $($c$)5\mathrm{.}29$ m